MinT - Best Known (107−33, 107, s)-Nets in Base 4

Best Known (107−33, 107, s)-Nets in Base 4

(107−33, 107, 240)-Net over F₄ — Constructive and digital

Digital (74, 107, 240)-net over F₄, using

t-expansion [i] based on digital (73, 107, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (73, 108, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 36, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(107−33, 107, 452)-Net over F₄ — Digital

Digital (74, 107, 452)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−33, 107, 22070)-Net in Base 4 — Upper bound on s

There is no (74, 107, 22071)-net in base 4, because

1 times m-reduction [i] would yield (74, 106, 22071)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6584 320226 273641 328264 898318 457210 465717 742951 582641 867985 029819 > 4¹⁰⁶ [i]